An American option is a contract between the option holder and option writer in which they agree on the right to buy or sell the underlying asset at a predetermined strike price on someday in the future no later than the option expiration date. In theory, an American call option on a non-dividend paying stock should never be exercised before its expiration day, hence it is always better to sell it rather than exercising it. Financial practice shows that many American call options are exercised early. In this diploma thesis, we present an empirical study that reveals a widespread of early exercises and tries to relate them to financial frictions observed in the markets, such as short-sale costs and transaction costs, which are typically disregarded in the classical models. Then we describe a discrete and a continuous market model that take financial frictions into account and allow us to derive the lower exercise boundary of an option. This is the critical stock price above which early exercise of an American call option is rational. The lower exercise boundary decreases as the short-sale costs, funding costs, and the required maintenance margins for options and stocks increase. We conclude the thesis by demonstrating that the proposed continuous model efficiently explains early options exercises in real financial markets.
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